Abstract
This paper considers the optimal investment problem in a financial market with one risk-free asset and one jump-diffusion risky asset. It is assumed that the insurance risk process is driven by a compound Poisson process and the two jump number processes are correlated by a common shock. A general mean-variance optimization problem is investigated, that is, besides the objective of terminal condition, the quadratic optimization functional includes also a running penalizing cost, which represents the deviations of the insurer’s wealth from a desired profit-solvency goal. By solving the Hamilton-Jacobi-Bellman (HJB) equation, we derive the closed-form expressions for the value function, as well as the optimal strategy. Moreover, under suitable assumption on model parameters, our problem reduces to the classical mean-variance portfolio selection problem and the efficient frontier is obtained.
Highlights
In the past two decades, the problems of optimal investment and optimal reinsurance have gained rich attention in actuarial and financial literature
Bäuerle (2005) first put forward that the criterion of mean-variance may be attractive in insurance applications and investigated optimal reinsurance strategy when the insurance risk process is described by a classical compound Poisson process
The second frequently-used model describes that financial market and insurance risk are dependent with each other, i.e., the risky asset and insurance claims are correlated by a common shock
Summary
In the past two decades, the problems of optimal investment and optimal reinsurance have gained rich attention in actuarial and financial literature. The second frequently-used model describes that financial market and insurance risk are dependent with each other, i.e., the risky asset and insurance claims are correlated by a common shock Based on this kind of common shock, Liang et al (2016, 2017) studied the optimal reinsurance-investment problems under the mean-variance and exponential utility criterion, respectively. Zhang and Liang (2017) investigated the optimal investment strategy under the criterion of maximizing the mean-variance utility with state dependent risk aversion. This paper considers a running penalizing cost, with a deterministic goal process to be achieved for the insurer and extends the existing results of the classical mean-variance problem As is known, this results in the optimization problem with wealth-path dependence (see Bouchard and Pham (2004)).
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